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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 \boxed{\frac{27}{16}}

📌 Question:** In a right triangle, the hypotenuse is \(c\) and the radius of the inscribed circle is \(r\). If the area of the triangle is \(A\), express the ratio \(\frac{A}{r^2}\) in terms of \(c\).

📌 For a right triangle with legs \(a\), \(b\), hypotenuse \(c\), and inradius \(r\), the area \(A\) is:

📌 The semiperimeter \(s\) is:

📌 s = \frac{a + b + c}{2}

📌 The inradius is related to area by:

📌 A = r \cdot s \quad \Rightarrow \quad r = \frac{A}{s}

📌 We want to compute \(\frac{A}{r^2}\):

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